As explained in the previous two answers, an extended metaphor is a metaphor that is carried out through most or all of a literary work. In Langston Hughes's poem "Mother to Son," Langston Hughes compares a mother's lifetime of struggles to her courage to perceive. In the intro to the poem, the mother explains to her son,
Life for me ain't been no crystal stair. Its had tacks in it, and splinters, and boards torn up. And places with no carpets on the floor, bare.
The mother in the poem compares her life to all of the glorious things that it is not. She begins by comparing her life to crystal stairs. Crystal is seen as beautiful, pure, clear and valuable. The mother explains that her life is not any of these things. She also showcases her life as being bare, filled with splinters and torn up boards. But Langston Hughes also shows this mother's refusal to give up and stop, and makes the case for fighting through even the unknown as seen below.
I'se still climbing on, and reachin landins, and sometimes, going in the dark where there ain't been no light.
The entire poem by Langston Hughes is one metaphor; this is why it is called an extended metaphor. The unstated comparison is between life and a set of steps that has by no means been "crystal"—a metaphor itself meaning that the stairs do not belong to a person whose life has been privileged (only well-to-do people own crystal glassware; a crystal staircase would indeed be extravagant).
This extended metaphor of a stairway is an apt one as often life is marked by stages and by a person's having elevated him/herself (e.g."climbing the ladder" to success or some other goal). While the mother may not have reached much success because of her social setting, she has always persevered nevertheless. This is the lesson that she wishes to teach her son:
But all the timeI’se been a-climbin’ on,And reachin’ landin’s,And turnin’ corners,And sometimes goin’ in the darkWhere there ain’t been no light.
Don’t you fall now—For I’se still goin’, honey
An extended metaphor is a metaphor that is continued throughout the text, whose meaning is central to the understanding of that text. In this poem, the extended metaphor concerns the mother's description of what life has been like for her and how it has been very challenging. Note how she introduces the extended metaphor in the following quote:
Life for me ain't been no crystal stair.
It's had tacks in it,
And boards torn up,
And places with no carpet on the floor—
The extended metaphor is therefore that life is compared to a staircase that is not a "crystal stair" but a very rough and painful staircase that has made it hard to continue to go upwards. However, inspite of these difficulties and the "splinters" and lack of furnishings, the mother in this poem has continued to ascend that staircase, and she urges her son to do the same and follow her example even though life may not be a "crystal stair."